A Sequential Bayesian Approach for Hydrologic Model Selection, Combination, and Predictions

Recently there is a growing popularity of using multiple models in ensemble hydrologic forecasting. In those approaches, a large number of models are selected, with each model being initialized for specific behavior. Because there is no such a model which performs well at all times, it is important to identify the strength of each model and provide an effective strategy in selecting model/models under new available observations. To achieve the fast tracking of model behavior with small errors, we have adopted a Bayesain sequential simulation method to the model selection and to the combination of multiple model estimates. The proposed approach, Bayesian Combined Prediction (BPC), is based on the probabilistic concept of conditional probability and Bayes' rule. It calculates posterior probability of each model being selected and also provides model estimates by mixture or switch between the models according to their posterior probability distribution. The recursive Bayes scheme enables its update of the posterior probability of each model and predictions in real-time, based on the models' predictive accuracy. The case study demonstrated the implementation of BPC in the model combination and selection in rainfall runoff processing. Several hydrologic modeling groups, including linear time series autoregressive-moving average models, nonlinear neural network models, and Sacramento Soil-Moisture Accounting model were tested. Simulation was conducted based on 25 years of daily rainfall-runoff data from the Leaf-River Basin near Collins Mississippi, USA. The posterior distribution of models at each simulation time step shows the preference of model selection under model combination. The performance of all individual models is compared with performance of the combined multiple model and the switching model (e.g. the maximum a posterior) at each time step. Several skill scores were used in the model evaluation. The validation shows that both multi-model combination and switch model solutions consistently outperform those of individual models. In addition, the time evolution of the posterior distribution of models provides further insights into the capability of models over several dominating hydrologic periods, such as precipitation driving, flow recession, and low flow periods.